Читать книгу Semiconductor Basics - George Domingo - Страница 13

Before I start, I want to clarify the terms used to define a wave, which I use in the next few sections, and the relations between these terms (see Figure 1.1). There are four variables that we use to define any sinusoidal wave:

 The amplitude, A: How high each peak of the wave is in relation to the middle, its zero value.

 The frequency, f: The number of ups and downs in the wave in a given time. The units are Hertz or number of ups and downs per second: a number/s.

 The wavelength, λ: The distance between two peaks, in meters (m), centimeters (cm), or micrometers (μm).

 The wave number, ν (the Greek letter nu, not the letter v): The reciprocal of the wavelength. Some properties of waves are better expressed by the reciprocal of the wavelength. The units are therefore 1/m or m−1, or cm−1, or μm−1.

The last three variables are related by the velocity of the wave. Velocity is the distance that a moving object covers during a fixed amount of time, so the velocity v (this is now the letter v) has units of meters per second (m/s). The key relationships are

(1.1)

and the wave number – the reciprocal of the wavelength – is

(1.2)

For example, suppose that Figure 1.1 represents a sound wave. The velocity of sound in air is 343 m s⁻¹. Take a look at Figure 1.1:

 The figure shows 5 cycles in 0.001 seconds, which means the frequency is 5000 cycles per second or f = 5000 Hz, (where Hz, Hertz is the unit for frequency) which happens to be the middle of our hearing range.

 The wavelength is the velocity divided by the frequency, or λ = 343 (m s−1)/5000 (1 s−1) = 0.069 m or 6.9 cm. Notice that the seconds cancel out, and therefore the units are in meters or centimeters.

 The wave number is v = 1/0.069 m = 14.5 m−1.

As much as possible, I use the metric system of units (MKS, meter, kilogram, second). I have always found it very annoying when books keep changing the unit system. When necessary, I will give you the equivalents.

Figure 1.1 A sinusoidal wave is described in several ways: frequency, wavelength, and reciprocal of the wavelength plus its amplitude.

Now we are ready to dive into the pre‐history of the Bohr atom and understand how Dr. Bohr came up with his famous model.